double run_soft_sphere(double reduced_density, double temp) {
Functional f = SoftFluid(sigma, 1, 0);
const double mu = find_chemical_potential(OfEffectivePotential(f), temp, reduced_density*pow(2,-5.0/2.0));
printf("mu is %g for reduced_density = %g at temperature %g\n", mu, reduced_density, temp);
//printf("Filling fraction is %g with functional %s at temperature %g\n", reduced_density, teff);
//fflush(stdout);
temperature = temp;
//if (kT == 0) kT = ;1
Lattice lat(Cartesian(xmax,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid softspherepotential(gd);
softspherepotential.Set(soft_sphere_potential);
f = SoftFluid(sigma, 1, mu); // compute approximate energy with chemical potential mu
const double approx_energy = f(temperature, reduced_density*pow(2,-5.0/2.0))*xmax*ymax*zmax;
const double precision = fabs(approx_energy*1e-9);
f = OfEffectivePotential(SoftFluid(sigma, 1, mu) + ExternalPotential(softspherepotential));
static Grid *potential = 0;
potential = new Grid(gd);
*potential = softspherepotential - temperature*log(reduced_density*pow(2,-5.0/2.0)/(1.0*radius*radius*radius))*VectorXd::Ones(gd.NxNyNz); // Bad starting guess
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, temperature);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, temperature,
potential,
QuadraticLineMinimizer));
took("Setting up the variables");
for (int i=0; min.improve_energy(true) && i<100; i++) {
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(temperature, gd, *potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, reduced_density);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/radial-wca-%06.4f-%04.2f.dat", temp, reduced_density);
z_plot(plotname, Grid(gd, pow(2,5.0/2.0)*density));
free(plotname);
{
//double peak = peak_memory()/1024.0/1024;
//double current = current_memory()/1024.0/1024;
//printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
took("Plotting stuff");
printf("density %g gives ff %g for reduced_density = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, reduced_density, temp);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
int main(int, char **) {
FILE *o = fopen("paper/figs/constrained-water.dat", "w");
Functional f = OfEffectivePotential(SaftFluidSlow(water_prop.lengthscale,
water_prop.epsilonAB, water_prop.kappaAB,
water_prop.epsilon_dispersion,
water_prop.lambda_dispersion, water_prop.length_scaling, 0));
double mu_satp = find_chemical_potential(f, water_prop.kT,
water_prop.liquid_density);
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.1);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint,
OfEffectivePotential(SaftFluidSlow(water_prop.lengthscale,
water_prop.epsilonAB, water_prop.kappaAB,
water_prop.epsilon_dispersion,
water_prop.lambda_dispersion, water_prop.length_scaling, mu_satp)));
Minimizer min = Precision(0, PreconditionedConjugateGradient(f, gd, water_prop.kT, &potential,
QuadraticLineMinimizer));
potential = water_prop.liquid_density*constraint
+ water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
//potential = water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
potential = -water_prop.kT*potential.cwise().log();
const int numiters = 50;
for (int i=0;i<numiters && min.improve_energy(true);i++) {
fflush(stdout);
Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
density.epsNative1d("paper/figs/1d-constrained-plot.eps",
Cartesian(0,0,0), Cartesian(0,0,zmax),
water_prop.liquid_density, 1, "Y axis: , x axis: ");
}
min.print_info();
double energy = min.energy()/width/width;
printf("Energy is %.15g\n", energy);
double N = 0;
{
Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) N += density[i]*gd.dvolume;
}
N = N/width/width;
printf("N is %.15g\n", N);
Grid density(gd, EffectivePotentialToDensity()(water_prop.kT, gd, potential));
density.epsNative1d("paper/figs/1d-constrained-plot.eps", Cartesian(0,0,0), Cartesian(0,0,zmax), water_prop.liquid_density, 1, "Y axis: , x axis: ");
//potential.epsNative1d("hard-wall-potential.eps", Cartesian(0,0,0), Cartesian(0,0,zmax), 1, 1);
fclose(o);
}
double run_walls(double reduced_density, const char *name, Functional fhs, double teff) {
double kT = teff;
if (kT == 0) kT = 1;
Functional f = OfEffectivePotential(fhs);
const double zmax = width + 2*spacing;
Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint, f);
Grid potential(gd);
potential = pow(2,-5.0/2.0)*(reduced_density*constraint + 1e-4*reduced_density*VectorXd::Ones(gd.NxNyNz));
potential = -kT*potential.cwise().log();
const double approx_energy = fhs(kT, reduced_density*pow(2,-5.0/2.0))*dw*dw*width;
const double precision = fabs(approx_energy*1e-11);
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, kT,
&potential,
QuadraticLineMinimizer));
took("Setting up the variables");
if (strcmp(name, "hard") != 0 && false) {
printf("For now, SoftFluid doesn't work properly, so we're skipping the\n");
printf("minimization at temperature %g.\n", teff);
} else {
for (int i=0;min.improve_energy(false) && i<100;i++) {
}
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(kT, gd, potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, reduced_density);
z_plot(plotname, Grid(gd, density*pow(2,5.0/2.0)));
free(plotname);
took("Plotting stuff");
printf("density %g gives ff %g for reduced density = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, reduced_density, teff);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
bool ConjugateGradientType::improve_energy(bool verbose) {
iter++;
//printf("I am running ConjugateGradient::improve_energy\n");
const double E0 = energy();
if (E0 != E0) {
// There is no point continuing, since we're starting with a NaN!
// So we may as well quit here.
if (verbose) {
printf("The initial energy is a NaN, so I'm quitting early from ConjugateGradientType::improve_energy.\n");
f.print_summary("has nan:", E0);
fflush(stdout);
}
return false;
}
double gdotd;
{
const VectorXd g = -grad();
// Let's immediately free the cached gradient stored internally!
invalidate_cache();
// Note: my notation vaguely follows that of
// [wikipedia](http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method).
// I use the Polak-Ribiere method, with automatic direction reset.
// Note that we could save some memory by using Fletcher-Reeves, and
// it seems worth implementing that as an option for
// memory-constrained problems (then we wouldn't need to store oldgrad).
double beta = g.dot(g - oldgrad)/oldgradsqr;
oldgrad = g;
if (beta < 0 || beta != beta || oldgradsqr == 0) beta = 0;
oldgradsqr = oldgrad.dot(oldgrad);
direction = g + beta*direction;
gdotd = oldgrad.dot(direction);
if (gdotd < 0) {
direction = oldgrad; // If our direction is uphill, reset to gradient.
if (verbose) printf("reset to gradient...\n");
gdotd = oldgrad.dot(direction);
}
}
Minimizer lm = linmin(f, gd, kT, x, direction, -gdotd, &step);
for (int i=0; i<100 && lm.improve_energy(verbose); i++) {
if (verbose) lm.print_info("\t");
}
if (verbose) {
//lm->print_info();
print_info();
printf("grad*dir/oldgrad*dir = %g\n", grad().dot(direction)/gdotd);
}
return (energy() < E0);
}
bool PreconditionedConjugateGradientType::improve_energy(bool verbose) {
iter++;
//printf("I am running ConjugateGradient::improve_energy\n");
const double E0 = energy();
if (isnan(E0)) {
// There is no point continuing, since we're starting with a NaN!
// So we may as well quit here.
if (verbose) {
printf("The initial energy is a NaN, so I'm quitting early.\n");
fflush(stdout);
}
return false;
}
double beta;
{
// Note: my notation vaguely follows that of
// [wikipedia](http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method).
// I use the Polak-Ribiere method, with automatic direction reset.
// Note that we could save some memory by using Fletcher-Reeves, and
// it seems worth implementing that as an option for
// memory-constrained problems (then we wouldn't need to store oldgrad).
pgrad(); // compute pgrad first, since that computes both.
beta = -pgrad().dot(-grad() - oldgrad)/oldgradsqr;
oldgrad = -grad();
if (beta < 0 || beta != beta || oldgradsqr == 0) beta = 0;
if (verbose) printf("beta = %g\n", beta);
oldgradsqr = -pgrad().dot(oldgrad);
direction = -pgrad() + beta*direction;
// Let's immediately free the cached gradient stored internally!
invalidate_cache();
} // free g and pg!
const double gdotd = oldgrad.dot(direction);
Minimizer lm = linmin(f, gd, kT, x, direction, -gdotd, &step);
for (int i=0; i<100 && lm.improve_energy(verbose); i++) {
if (verbose) lm.print_info("\t");
}
if (verbose) {
//lm->print_info();
print_info();
printf("grad*oldgrad = %g\n", grad().dot(direction)/gdotd);
}
return (energy() < E0 || beta != 0);
}
void run_with_eta(double eta, const char *name, Functional fhs) {
// Generates a data file for the pair distribution function, for filling fraction eta
// and distance of first sphere from wall of z0. Data saved in a table such that the
// columns are x values and rows are z1 values.
printf("Now starting run_with_eta with eta = %g name = %s\n",
eta, name);
Functional f = OfEffectivePotential(fhs + IdealGas());
double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
f = OfEffectivePotential(fhs + IdealGas()
+ ChemicalPotential(mu));
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width));
GridDescription gd(lat, dx);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinsphere);
f = constrain(constraint, f);
potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
potential = -potential.cwise().log();
const double approx_energy = (fhs + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*uipow(width,3);
const double precision = fabs(approx_energy*1e-10);
//printf("Minimizing to %g absolute precision...\n", precision);
{ // Put mimizer in block so as to free it when we finish minimizing to save memory.
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, 1,
&potential,
QuadraticLineMinimizer));
for (int i=0;min.improve_energy(true) && i<100;i++) {
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
took("Doing the minimization");
}
Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
Grid gsigma(gd, gSigmaA(1.0)(1, gd, density));
Grid nA(gd, ShellConvolve(2)(1, density)/(4*M_PI*4));
Grid n3(gd, StepConvolve(1)(1, density));
Grid nbar_sokolowski(gd, StepConvolve(1.6)(1, density));
nbar_sokolowski /= (4.0/3.0*M_PI*ipow(1.6, 3));
// Create the walls directory if it doesn't exist.
if (mkdir("papers/pair-correlation/figs/walls", 0777) != 0 && errno != EEXIST) {
// We failed to create the directory, and it doesn't exist.
printf("Failed to create papers/pair-correlation/figs/walls: %s",
strerror(errno));
exit(1); // fail immediately with error code
}
// here you choose the values of z0 to use
// dx is the resolution at which we compute the density.
char *plotname = new char[4096];
for (double z0 = 2.1; z0 < 4.5; z0 += 2.1) {
// For each z0, we now pick one of our methods for computing the
// pair distribution function:
for (int version = 0; version < numplots; version++) {
sprintf(plotname,
"papers/pair-correlation/figs/triplet%s-%s-%04.2f-%1.2f.dat",
name, fun[version], eta, z0);
FILE *out = fopen(plotname,"w");
FILE *xfile = fopen("papers/pair-correlation/figs/triplet-x.dat","w");
FILE *zfile = fopen("papers/pair-correlation/figs/triplet-z.dat","w");
// the +1 for z0 and z1 are to shift the plot over, so that a sphere touching the wall
// is at z = 0, to match with the monte carlo data
const Cartesian r0(0,0,z0);
for (double x = 0; x < 4; x += dx) {
for (double z1 = -4; z1 <= 9; z1 += dx) {
const Cartesian r1(x,0,z1);
double g2 = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out, "%g\t", g3);
fprintf(xfile, "%g\t", x);
fprintf(zfile, "%g\t", z1);
}
fprintf(out, "\n");
fprintf(xfile, "\n");
fprintf(zfile, "\n");
}
fclose(out);
fclose(xfile);
fclose(zfile);
}
}
delete[] plotname;
took("Dumping the triplet dist plots");
const double ds = 0.01; // step size to use in path plots, FIXME increase for publication!
const double delta = .1; //this is the value of radius of the
//particle as it moves around the contact
//sphere on its path
char *plotname_path = new char[4096];
for (int version = 0; version < numplots; version++) {
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet%s-path-%s-%04.2f.dat",
name, fun[version], eta);
FILE *out_path = fopen(plotname_path, "w");
if (!out_path) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-back-contact-%s-%04.2f.dat",
fun[version], eta);
FILE *out_back = fopen(plotname_path, "w");
if (!out_back) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
fprintf(out_path, "# unused\tg3\tz\tx\n");
fprintf(out_back, "# unused\tg3\tz\tx\n");
const Cartesian r0(0,0, 2.0+delta);
const double max_theta = M_PI*2.0/3;
for (double z = 7; z >= 2*(2.0 + delta); z-=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double z = -7; z <= -(2.0 + delta); z+=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
const double dtheta = ds/2;
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, (2.0+delta)*(1+cos(theta)));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0,-(2.0+delta)*cos(theta));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double x = (2.0+delta)*sqrt(3)/2; x<=6; x+=ds){
const Cartesian r1(x, 0, 1.0+delta/2);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
fclose(out_path);
fclose(out_back);
}
for (int version = 0; version < numplots; version++) {
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-path-inbetween-%s-%04.2f.dat",
fun[version], eta);
FILE *out_path = fopen(plotname_path, "w");
if (!out_path) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
sprintf(plotname_path,
"papers/pair-correlation/figs/triplet-back-inbetween-%s-%04.2f.dat",
fun[version], eta);
FILE *out_back = fopen(plotname_path, "w");
if (!out_back) {
fprintf(stderr, "Unable to create file %s!\n", plotname_path);
return;
}
fprintf(out_path, "# unused\tg3\tz\tx\n");
fprintf(out_back, "# unused\tg3\tz\tx\n");
const Cartesian r0(0,0, 4.0+2*delta);
const double max_theta = M_PI;
for (double z = 11; z >= 3*(2.0 + delta); z-=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double z = -10; z <= -(2.0 + delta); z+=ds) {
const Cartesian r1(0,0,z);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
const double dtheta = ds/2;
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, (2.0+delta)*(2+cos(theta)));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double theta = 0; theta <= max_theta; theta += dtheta){
const Cartesian r1((2.0+delta)*sin(theta), 0, -(2.0+delta)*cos(theta));
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
for (double x = 0; x>=-6; x-=ds){
const Cartesian r1(x, 0, 2.0+delta);
double g2_path = pairdists[version](gsigma, density, nA, n3, nbar_sokolowski, r0, r1);
double n_bulk = (3.0/4.0/M_PI)*eta;
double g3 = g2_path*density(r0)*density(r1)/n_bulk/n_bulk;
fprintf(out_path,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
fprintf(out_back,"0\t%g\t%g\t%g\n", g3, r1[2], r1[0]);
}
fclose(out_path);
fclose(out_back);
}
delete[] plotname_path;
}
double run_walls(double eta, const char *name, Functional fhs, double teff) {
//printf("Filling fraction is %g with functional %s at temperature %g\n", eta, name, teff);
//fflush(stdout);
double kT = teff;
if (kT == 0) kT = 1;
Functional f = OfEffectivePotential(fhs);
const double zmax = width + 2*spacing;
Lattice lat(Cartesian(dw,0,0), Cartesian(0,dw,0), Cartesian(0,0,zmax));
GridDescription gd(lat, dx);
Grid constraint(gd);
constraint.Set(notinwall);
f = constrain(constraint, f);
// We reuse the potential, which should give us a better starting
// guess on each calculation.
static Grid *potential = 0;
if (strcmp(name, "hard") == 0) {
// start over for each potential
delete potential;
potential = 0;
}
if (!potential) {
potential = new Grid(gd);
*potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
*potential = -kT*potential->cwise().log();
}
// FIXME below I use the HS energy because of issues with the actual
// functional.
const double approx_energy = fhs(kT, eta/(4*M_PI/3))*dw*dw*width;
const double precision = fabs(approx_energy*1e-5);
printf("\tMinimizing to %g absolute precision from %g from %g...\n", precision, approx_energy, kT);
fflush(stdout);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, kT,
potential,
QuadraticLineMinimizer));
took("Setting up the variables");
for (int i=0;min.improve_energy(false) && i<100;i++) {
}
took("Doing the minimization");
min.print_info();
Grid density(gd, EffectivePotentialToDensity()(kT, gd, *potential));
//printf("# per area is %g at filling fraction %g\n", density.sum()*gd.dvolume/dw/dw, eta);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/fuzzy-fmt/figs/walls%s-%06.4f-%04.2f.dat", name, teff, eta);
z_plot(plotname, Grid(gd, 4*M_PI*density/3));
free(plotname);
{
GridDescription gdj = density.description();
double sep = gdj.dz*gdj.Lat.a3().norm();
int div = gdj.Nz;
int mid = int (div/2.0);
double Ntot_per_A = 0;
double mydist = 0;
for (int j=0; j<mid; j++){
Ntot_per_A += density(0,0,j)*sep;
mydist += sep;
}
double Extra_per_A = Ntot_per_A - eta/(4.0/3.0*M_PI)*width/2;
FILE *fout = fopen("papers/fuzzy-fmt/figs/wallsfillingfracInfo.txt", "a");
fprintf(fout, "walls%s-%04.2f.dat - If you want to match the bulk filling fraction of figs/walls%s-%04.2f.dat, than the number of extra spheres per area to add is %04.10f. So you'll want to multiply %04.2f by your cavity volume and divide by (4/3)pi. Then add %04.10f times the Area of your cavity to this number\n",
name, eta, name, eta, Extra_per_A, eta, Extra_per_A);
int wallslen = 20;
double Extra_spheres = (eta*wallslen*wallslen*wallslen/(4*M_PI/3) + Extra_per_A*wallslen*wallslen);
fprintf (fout, "For filling fraction %04.02f and walls of length %d you'll want to use %.0f spheres.\n\n", eta, wallslen, Extra_spheres);
fclose(fout);
}
{
//double peak = peak_memory()/1024.0/1024;
//double current = current_memory()/1024.0/1024;
//printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
took("Plotting stuff");
printf("density %g gives ff %g for eta = %g and T = %g\n", density(0,0,gd.Nz/2),
density(0,0,gd.Nz/2)*4*M_PI/3, eta, teff);
return density(0, 0, gd.Nz/2)*4*M_PI/3; // return bulk filling fraction
}
int main(int argc, char *argv[]) {
if (argc > 1) {
if (sscanf(argv[1], "%lg", &diameter) != 1) {
printf("Got bad argument: %s\n", argv[1]);
return 1;
}
diameter *= nm;
using_default_diameter = false;
printf("Diameter is %g bohr\n", diameter);
}
const double ptransition =(3.0*M_PI-4.0)*(diameter/2.0)/2.0;
const double dmax = ptransition + 0.6*nm;
double zmax = 2*diameter+dmax+2*nm;
double ymax = 2*diameter+dmax+2*nm;
char *datname = new char[1024];
snprintf(datname, 1024, "papers/water-saft/figs/four-rods-in-water-%04.1fnm.dat", diameter/nm);
FILE *o = fopen(datname, "w");
delete[] datname;
Functional f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
new_water_prop.epsilonAB, new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling, 0));
double n_1atm = pressure_to_density(f, new_water_prop.kT, atmospheric_pressure,
0.001, 0.01);
double mu_satp = find_chemical_potential(f, new_water_prop.kT, n_1atm);
f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
new_water_prop.epsilonAB, new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling, mu_satp));
const double EperVolume = f(new_water_prop.kT, -new_water_prop.kT*log(n_1atm));
const double EperCell = EperVolume*(zmax*ymax - 4*0.25*M_PI*diameter*diameter)*width;
//Functional X = Xassociation(new_water_prop.lengthscale, new_water_prop.epsilonAB,
// new_water_prop.kappaAB, new_water_prop.epsilon_dispersion,
// new_water_prop.lambda_dispersion,
// new_water_prop.length_scaling);
Functional S = OfEffectivePotential(EntropySaftFluid2(new_water_prop.lengthscale,
new_water_prop.epsilonAB,
new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling));
//dmax, dstep already in bohrs (so it doesn't need to be converted from nm)
double dstep = 0.25*nm;
for (distance=0.0*nm; distance<=dmax; distance += dstep) {
if ((distance >= ptransition - 0.5*nm) && (distance <= ptransition + 0.05*nm)) {
if (distance >= ptransition - 0.25*nm) {
dstep = 0.03*nm;
} else {
dstep = 0.08*nm;
}
} else {
dstep = 0.25*nm;
}
Lattice lat(Cartesian(width,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.2);
printf("Grid is %d x %d x %d\n", gd.Nx, gd.Ny, gd.Nz);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
f = OfEffectivePotential(WaterSaft(new_water_prop.lengthscale,
new_water_prop.epsilonAB, new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling, mu_satp));
f = constrain(constraint, f);
printf("Diameter is %g bohr (%g nm)\n", diameter, diameter/nm);
printf("Distance between rods = %g bohr (%g nm)\n", distance, distance/nm);
potential = new_water_prop.liquid_density*constraint
+ 400*new_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
//potential = new_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
potential = -new_water_prop.kT*potential.cwise().log();
const double surface_tension = 5e-5; // crude guess from memory...
const double surfprecision = 1e-5*(4*M_PI*diameter)*width*surface_tension; // five digits accuracy
const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision for small rods
const double precision = bulkprecision + surfprecision;
printf("Precision limit from surface tension is to %g based on %g and %g\n",
precision, surfprecision, bulkprecision);
Minimizer min = Precision(precision, PreconditionedConjugateGradient(f, gd, new_water_prop.kT,
&potential,
QuadraticLineMinimizer));
const int numiters = 200;
for (int i=0;i<numiters && min.improve_energy(false);i++) {
fflush(stdout);
// {
// double peak = peak_memory()/1024.0/1024;
// double current = current_memory()/1024.0/1024;
// printf("Peak memory use is %g M (current is %g M)\n", peak, current);
// }
}
Grid potential2(gd);
Grid constraint2(gd);
constraint2.Set(notinmiddle);
potential2 = new_water_prop.liquid_density*(constraint2.cwise()*constraint)
+ 400*new_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
potential2 = -new_water_prop.kT*potential2.cwise().log();
Minimizer min2 = Precision(1e-12, PreconditionedConjugateGradient(f, gd, new_water_prop.kT,
&potential2,
QuadraticLineMinimizer));
for (int i=0;i<numiters && min2.improve_energy(false);i++) {
fflush(stdout);
// {
// double peak = peak_memory()/1024.0/1024;
// double current = current_memory()/1024.0/1024;
// printf("Peak memory use is %g M (current is %g M)\n", peak, current);
// }
}
char *plotnameslice = new char[1024];
snprintf(plotnameslice, 1024, "papers/water-saft/figs/four-rods-%04.1f-%04.2f.dat", diameter/nm, distance/nm);
printf("The bulk energy per cell should be %g\n", EperCell);
double energy;
if (min.energy() < min2.energy()) {
energy = (min.energy() - EperCell)/width;
Grid density(gd, EffectivePotentialToDensity()(new_water_prop.kT, gd, potential));
printf("Using liquid in middle initially.\n");
plot_grids_yz_directions(plotnameslice, density);
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
} else {
energy = (min2.energy() - EperCell)/width;
Grid density(gd, EffectivePotentialToDensity()(new_water_prop.kT, gd, potential2));
printf("Using vapor in middle initially.\n");
plot_grids_yz_directions(plotnameslice, density);
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
}
printf("Liquid energy is %.15g. Vapor energy is %.15g\n", min.energy(), min2.energy());
fprintf(o, "%g\t%.15g\n", distance/nm, energy);
//Grid entropy(gd, S(new_water_prop.kT, potential));
//Grid Xassoc(gd, X(new_water_prop.kT, density));
//plot_grids_y_direction(plotnameslice, density, energy_density, entropy, Xassoc);
//Grid energy_density(gd, f(new_water_prop.kT, gd, potential));
delete[] plotnameslice;
}
fclose(o);
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
}
double surface_tension(Minimizer min, Functional f0, LiquidProperties prop,
bool verbose, const char *plotname) {
int numptspersize = 100;
int size = 64;
const int gas_size = 10;
Lattice lat(Cartesian(1,0,0), Cartesian(0,1,0), Cartesian(0,0,size*prop.lengthscale));
GridDescription gd(lat, 1, 1, numptspersize*size);
Grid potential(gd);
// Set the density to range from vapor to liquid
const double Veff_liquid = -prop.kT*log(prop.liquid_density);
const double Veff_gas = -prop.kT*log(prop.vapor_density);
for (int i=0; i<gd.NxNyNz*gas_size/size; i++) potential[i] = Veff_gas;
for (int i=gd.NxNyNz*gas_size/size; i<gd.NxNyNz; i++) potential[i] = Veff_liquid;
// Enable the following line for debugging...
//f0.run_finite_difference_test("f0", prop.kT, potential);
min.minimize(f0, gd, &potential);
while (min.improve_energy(verbose))
if (verbose) {
printf("Working on liberated interface...\n");
fflush(stdout);
}
const double Einterface = f0.integral(prop.kT, potential);
double Ninterface = 0;
Grid interface_density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) Ninterface += interface_density[i]*gd.dvolume;
if (verbose) printf("Got interface energy of %g.\n", Einterface);
for (int i=0; i<gd.NxNyNz; i++) potential[i] = Veff_gas;
min.minimize(f0, gd, &potential);
while (min.improve_energy(verbose))
if (verbose) {
printf("Working on gas...\n");
fflush(stdout);
}
const double Egas = f0.integral(prop.kT, potential);
double Ngas = 0;
{
Grid density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) Ngas += density[i]*gd.dvolume;
}
for (int i=0; i<gd.NxNyNz; i++) potential[i] = Veff_liquid;
if (verbose) {
printf("\n\n\nWorking on liquid...\n");
fflush(stdout);
}
min.minimize(f0, gd, &potential);
while (min.improve_energy(verbose))
if (verbose) {
printf("Working on liquid...\n");
fflush(stdout);
}
const double Eliquid = f0.integral(prop.kT, potential);
double Nliquid = 0;
{
Grid density(gd, EffectivePotentialToDensity()(prop.kT, gd, potential));
for (int i=0;i<gd.NxNyNz;i++) Nliquid += density[i]*gd.dvolume;
}
const double X = Ninterface/Nliquid; // Fraction of volume effectively filled with liquid.
const double surface_tension = (Einterface - Eliquid*X - Egas*(1-X))/2;
if (verbose) {
printf("\n\n");
printf("interface energy is %.15g\n", Einterface);
printf("gas energy is %.15g\n", Egas);
printf("liquid energy is %.15g\n", Eliquid);
printf("Ninterface/liquid/gas = %g/%g/%g\n", Ninterface, Nliquid, Ngas);
printf("X is %g\n", X);
printf("surface tension is %.10g\n", surface_tension);
}
if (plotname)
interface_density.Dump1D(plotname, Cartesian(0,0,0),
Cartesian(0,0,size*prop.lengthscale));
return surface_tension;
}
int main(int argc, char *argv[]) {
clock_t start_time = clock();
if (argc > 1) {
if (sscanf(argv[1], "%lg", &diameter) != 1) {
printf("Got bad argument: %s\n", argv[1]);
return 1;
}
diameter *= nm;
using_default_diameter = false;
}
printf("Diameter is %g bohr = %g nm\n", diameter, diameter/nm);
const double padding = 1*nm;
xmax = ymax = zmax = diameter + 2*padding;
char *datname = (char *)malloc(1024);
sprintf(datname, "papers/hughes-saft/figs/sphere-%04.2fnm-energy.dat", diameter/nm);
Functional f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, 0));
double n_1atm = pressure_to_density(f, hughes_water_prop.kT, atmospheric_pressure,
0.001, 0.01);
double mu_satp = find_chemical_potential(f, hughes_water_prop.kT, n_1atm);
f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu_satp));
Functional S = OfEffectivePotential(EntropySaftFluid2(new_water_prop.lengthscale,
new_water_prop.epsilonAB,
new_water_prop.kappaAB,
new_water_prop.epsilon_dispersion,
new_water_prop.lambda_dispersion,
new_water_prop.length_scaling));
const double EperVolume = f(hughes_water_prop.kT, -hughes_water_prop.kT*log(n_1atm));
const double EperNumber = EperVolume/n_1atm;
const double SperNumber = S(hughes_water_prop.kT, -hughes_water_prop.kT*log(n_1atm))/n_1atm;
const double EperCell = EperVolume*(zmax*ymax*xmax - (M_PI/6)*diameter*diameter*diameter);
//for (diameter=0*nm; diameter<3.0*nm; diameter+= .1*nm) {
Lattice lat(Cartesian(xmax,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.2);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu_satp));
f = constrain(constraint, f);
//constraint.epsNativeSlice("papers/hughes-saft/figs/sphere-constraint.eps",
// Cartesian(0,ymax,0), Cartesian(0,0,zmax),
// Cartesian(0,ymax/2,zmax/2));
//printf("Constraint has become a graph!\n");
potential = hughes_water_prop.liquid_density*constraint
+ 100*hughes_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
//potential = hughes_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
potential = -hughes_water_prop.kT*potential.cwise().log();
double energy;
{
const double surface_tension = 5e-5; // crude guess from memory...
const double surfprecision = 1e-4*M_PI*diameter*diameter*surface_tension; // four digits precision
const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision for small spheres
const double precision = bulkprecision + surfprecision;
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, hughes_water_prop.kT,
&potential,
QuadraticLineMinimizer));
printf("\nDiameter of sphere = %g bohr (%g nm)\n", diameter, diameter/nm);
const int numiters = 200;
for (int i=0;i<numiters && min.improve_energy(true);i++) {
//fflush(stdout);
//Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
//density.epsNativeSlice("papers/hughes-saft/figs/sphere.eps",
// Cartesian(0,ymax,0), Cartesian(0,0,zmax),
// Cartesian(0,ymax/2,zmax/2));
//sleep(3);
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
energy = min.energy();
printf("Total energy is %.15g\n", energy);
// Here we free the minimizer with its associated data structures.
}
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
double entropy = S.integral(hughes_water_prop.kT, potential);
Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
printf("Number of water molecules is %g\n", density.integrate());
printf("The bulk energy per cell should be %g\n", EperCell);
printf("The bulk energy based on number should be %g\n", EperNumber*density.integrate());
printf("The bulk entropy is %g/N\n", SperNumber);
Functional otherS = EntropySaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB,
hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling);
printf("The bulk entropy (haskell) = %g/N\n", otherS(hughes_water_prop.kT, n_1atm)/n_1atm);
//printf("My entropy is %g when I would expect %g\n", entropy, entropy - SperNumber*density.integrate());
double hentropy = otherS.integral(hughes_water_prop.kT, density);
otherS.print_summary(" ", hentropy, "total entropy");
printf("My haskell entropy is %g, when I would expect = %g, difference is %g\n", hentropy,
otherS(hughes_water_prop.kT, n_1atm)*density.integrate()/n_1atm,
hentropy - otherS(hughes_water_prop.kT, n_1atm)*density.integrate()/n_1atm);
FILE *o = fopen(datname, "w");
//fprintf(o, "%g\t%.15g\n", diameter/nm, energy - EperCell);
fprintf(o, "%g\t%.15g\t%.15g\t%.15g\t%.15g\n", diameter/nm, energy - EperNumber*density.integrate(), energy - EperCell,
hughes_water_prop.kT*(entropy - SperNumber*density.integrate()),
hughes_water_prop.kT*(hentropy - otherS(hughes_water_prop.kT, n_1atm)*density.integrate()/n_1atm));
fclose(o);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/hughes-saft/figs/sphere-%04.2f.dat", diameter/nm);
plot_grids_y_direction(plotname, density);
free(plotname);
//density.epsNativeSlice("papers/hughes-saft/figs/sphere.eps",
// Cartesian(0,ymax,0), Cartesian(0,0,zmax),
// Cartesian(0,ymax/2,zmax/2));
double peak = peak_memory()/1024.0/1024;
printf("Peak memory use is %g M\n", peak);
double oldN = density.integrate();
density = n_1atm*VectorXd::Ones(gd.NxNyNz);;
double hentropyb = otherS.integral(hughes_water_prop.kT, density);
printf("bulklike thingy has %g molecules\n", density.integrate());
otherS.print_summary(" ", hentropyb, "bulk-like entropy");
printf("entropy difference is %g\n", hentropy - hentropyb*oldN/density.integrate());
// }
clock_t end_time = clock();
double seconds = (end_time - start_time)/double(CLOCKS_PER_SEC);
double hours = seconds/60/60;
printf("Entire calculation took %.0f hours %.0f minutes\n", hours, 60*(hours-floor(hours)));
}
int main(int, char **) {
for (double eta = 0.3; eta < 0.35; eta += 0.1) {
// Generates a data file for the pair distribution function, for filling fraction eta
// and distance of first sphere from wall of z0. Data saved in a table such that the
// columns are x values and rows are z1 values.
printf("Now starting sphere_with_wall with eta = %g\n",eta);
Lattice lat(Cartesian(width,0,0), Cartesian(0,width,0), Cartesian(0,0,width+2*spacing));
GridDescription gd(lat, dx); //the resolution here dramatically affects our memory use
Functional f = OfEffectivePotential(WB + IdealGas());
double mu = find_chemical_potential(f, 1, eta/(4*M_PI/3));
f = OfEffectivePotential(WB + IdealGas()
+ ChemicalPotential(mu));
Grid potential(gd);
Grid constraint(gd);
constraint.Set(*notinwall_or_sphere);
constraint.epsNativeSlice("myconstraint.eps",
Cartesian(0, 0, 2*(width+2*spacing)),
Cartesian(2*width, 0, 0),
Cartesian(0, 0, 0));
f = constrain(constraint, f);
potential = (eta*constraint + 1e-4*eta*VectorXd::Ones(gd.NxNyNz))/(4*M_PI/3);
potential = -potential.cwise().log();
const double approx_energy = (WB + IdealGas() + ChemicalPotential(mu))(1, eta/(4*M_PI/3))*dw*dw*width;
const double precision = fabs(approx_energy*1e-4);
//printf("Minimizing to %g absolute precision...\n", precision);
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, 1,
&potential,
QuadraticLineMinimizer));
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
for (int i=0; min.improve_energy(true) && i<100; i++) {
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
Grid density(gd, EffectivePotentialToDensity()(1, gd, potential));
char *plotname = new char[1024];
sprintf(plotname, "papers/pair-correlation/figs/walls/wallsWB-sphere-dft-%04.2f.dat", eta);
pair_plot(plotname, density);
delete[] plotname;
char *plotname_path = new char[1024];
sprintf(plotname_path, "papers/pair-correlation/figs/walls/wallsWB-sphere-dft-path-%04.2f.dat", eta);
path_plot(plotname_path, density, constraint);
delete[] plotname_path;
fflush(stdout);
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
}
fflush(stdout);
}
fflush(stdout);
// Just create this file so make knows we have run.
if (!fopen("papers/pair-correlation/figs/walls_sphere.dat", "w")) {
printf("Error creating walls.dat!\n");
return 1;
}
fflush(stdout);
return 1;
}
int main(int argc, char *argv[]) {
clock_t start_time = clock();
if (argc == 3) {
if (sscanf(argv[2], "%lg", &temperature) != 1) {
printf("Got bad argument: %s\n", argv[2]);
return 1;
}
temperature *= kB;
bool good_element = false;
for (int i=0; i<numelements; i++) {
if (strcmp(elements[i], argv[1]) == 0) {
sigma = sigmas[i];
epsilon = epsilons[i];
good_element = true;
}
}
if (!good_element) {
printf("Bad element: %s\n", argv[1]);
return 1;
}
} else {
printf("Need element and temperature.\n");
return 1;
}
char *datname = (char *)malloc(1024);
sprintf(datname, "papers/water-saft/figs/hughes-lj-%s-%gK-energy.dat", argv[1], temperature/kB);
Functional f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, 0));
double n_1atm = pressure_to_density(f, temperature, lj_pressure,
0.001, 0.01);
double mu = find_chemical_potential(f, temperature, n_1atm);
f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu));
Functional S = OfEffectivePotential(EntropySaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB,
hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling));
const double EperVolume = f(temperature, -temperature*log(n_1atm));
const double EperNumber = EperVolume/n_1atm;
const double SperNumber = S(temperature, -temperature*log(n_1atm))/n_1atm;
const double EperCell = EperVolume*(zmax*ymax*xmax - (4*M_PI/3)*sigma*sigma*sigma);
Lattice lat(Cartesian(xmax,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.20);
Grid potential(gd);
Grid externalpotential(gd);
externalpotential.Set(externalpotentialfunction);
f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu) + ExternalPotential(externalpotential));
Functional X = WaterX(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu);
Functional HB = HughesHB(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu);
externalpotential.epsNativeSlice("papers/water-saft/figs/hughes-lj-potential.eps",
Cartesian(0,ymax,0), Cartesian(0,0,zmax),
Cartesian(0,ymax/2,zmax/2));
printf("Done outputting hughes-lj-potential.eps\n");
potential = 0*externalpotential - temperature*log(n_1atm)*VectorXd::Ones(gd.NxNyNz); // ???
double energy;
{
const double surface_tension = 5e-5; // crude guess from memory...
const double surfprecision = 1e-4*M_PI*sigma*sigma*surface_tension; // four digits precision
const double bulkprecision = 1e-12*fabs(EperCell); // but there's a limit on our precision
const double precision = (bulkprecision + surfprecision)*1e-6;
Minimizer min = Precision(precision,
PreconditionedConjugateGradient(f, gd, temperature,
&potential,
QuadraticLineMinimizer));
const int numiters = 200;
for (int i=0;i<numiters && min.improve_energy(true);i++) {
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
fflush(stdout);
{
char* name = new char[1000];
sprintf(name, "papers/water-saft/figs/hughes-lj-%s-%gK-density-%d.eps", argv[1], temperature/kB, i);
Grid density(gd, EffectivePotentialToDensity()(temperature, gd, potential));
density.epsNativeSlice(name,
Cartesian(0,ymax,0), Cartesian(0,0,zmax),
Cartesian(0,ymax/2,zmax/2));
}
Grid gradient(gd, potential);
gradient *= 0;
f.integralgrad(temperature, potential, &gradient);
char* gradname = new char[1000];
sprintf(gradname, "papers/water-saft/figs/hughes-lj-%s-%gK-gradient-%d.eps", argv[1], temperature/kB, i);
gradient.epsNativeSlice(gradname,
Cartesian(0,ymax,0), Cartesian(0,0,zmax),
Cartesian(0,ymax/2,zmax/2));
Grid density(gd, EffectivePotentialToDensity()(temperature, gd, potential));
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/water-saft/figs/hughes-lj-%s-%gK-%d.dat", argv[1], temperature/kB, i);
plot_grids_y_direction(plotname, density, gradient);
// Grid gradient(gd, potential);
// gradient *= 0;
// f.integralgrad(temperature, potential, &gradient);
// sprintf(name, "papers/water-saft/figs/lj-%s-%d-gradient-big.eps", argv[1], i);
// gradient.epsNativeSlice("papers/water-saft/figs/lj-gradient-big.eps",
// Cartesian(0,ymax,0), Cartesian(0,0,zmax),
// Cartesian(0,ymax/2,zmax/2));
// sprintf(name, "papers/water-saft/figs/lj-%s-%d-big.dat", argv[1], i);
// plot_grids_y_direction(name, density, gradient);
}
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
energy = min.energy();
printf("Total energy is %.15g\n", energy);
// Here we free the minimizer with its associated data structures.
}
{
double peak = peak_memory()/1024.0/1024;
double current = current_memory()/1024.0/1024;
printf("Peak memory use is %g M (current is %g M)\n", peak, current);
}
Grid gradient(gd, potential);
gradient *= 0;
f.integralgrad(temperature, potential, &gradient);
gradient.epsNativeSlice("papers/water-saft/figs/hughes-lj-gradient.eps",
Cartesian(0,ymax,0), Cartesian(0,0,zmax),
Cartesian(0,ymax/2,zmax/2));
double entropy = S.integral(temperature, potential);
Grid density(gd, EffectivePotentialToDensity()(temperature, gd, potential));
// Grid zeroed_out_density(gd, density.cwise()*constraint); // this is zero inside the sphere!
Grid X_values(gd, X(temperature, gd, density));
//Grid H_bonds_grid(gd, zeroed_out_density.cwise()*(4*(VectorXd::Ones(gd.NxNyNz)-X_values)));
//const double broken_H_bonds = (HB(temperature, n_1atm)/n_1atm)*zeroed_out_density.integrate() - H_bonds_grid.integrate();
//printf("Number of water molecules is %g\n", density.integrate());
printf("The bulk energy per cell should be %g\n", EperCell);
printf("The bulk energy based on number should be %g\n", EperNumber*density.integrate());
printf("The bulk entropy is %g/N\n", SperNumber);
Functional otherS = EntropySaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB,
hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling);
printf("The bulk entropy (haskell) = %g/N\n", otherS(temperature, n_1atm)/n_1atm);
//printf("My entropy is %g when I would expect %g\n", entropy, entropy - SperNumber*density.integrate());
double hentropy = otherS.integral(temperature, density);
otherS.print_summary(" ", hentropy, "total entropy");
printf("My haskell entropy is %g, when I would expect = %g, difference is %g\n", hentropy,
otherS(temperature, n_1atm)*density.integrate()/n_1atm,
hentropy - otherS(temperature, n_1atm)*density.integrate()/n_1atm);
FILE *o = fopen(datname, "w");
fprintf(o, "%g\t%.15g\t%.15g\t%.15g\n", temperature/kB, energy - EperNumber*density.integrate(),
temperature*(entropy - SperNumber*density.integrate()),
temperature*(hentropy - otherS(temperature, n_1atm)*density.integrate()/n_1atm));
fclose(o);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/water-saft/figs/hughes-lj-%s-%gK.dat", argv[1], temperature/kB);
//plot_grids_y_direction(plotname, density, X_values);
plot_grids_y_direction(plotname, density, gradient);
free(plotname);
double peak = peak_memory()/1024.0/1024;
printf("Peak memory use is %g M\n", peak);
double oldN = density.integrate();
density = n_1atm*VectorXd::Ones(gd.NxNyNz);;
double hentropyb = otherS.integral(temperature, density);
printf("bulklike thingy has %g molecules\n", density.integrate());
otherS.print_summary(" ", hentropyb, "bulk-like entropy");
printf("entropy difference is %g\n", hentropy - hentropyb*oldN/density.integrate());
clock_t end_time = clock();
double seconds = (end_time - start_time)/double(CLOCKS_PER_SEC);
double hours = seconds/60/60;
printf("Entire calculation took %.0f hours %.0f minutes\n", hours, 60*(hours-floor(hours)));
}
int main(int, char **) {
FILE *o = fopen("papers/hughes-saft/figs/single-rod-in-water-low-res.dat", "w");
Functional f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, 0));
double n_1atm = pressure_to_density(f, hughes_water_prop.kT, atmospheric_pressure,
0.001, 0.01);
double mu_satp = find_chemical_potential(f, hughes_water_prop.kT, n_1atm);
f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu_satp));
const double EperVolume = f(hughes_water_prop.kT, -hughes_water_prop.kT*log(n_1atm));
for (cavitysize=1.0*nm; cavitysize<=1.1*nm; cavitysize += 0.5*nm) {
Lattice lat(Cartesian(width,0,0), Cartesian(0,ymax,0), Cartesian(0,0,zmax));
GridDescription gd(lat, 0.5);
Grid potential(gd);
Grid constraint(gd);
constraint.Set(notinwall);
f = OfEffectivePotential(SaftFluid2(hughes_water_prop.lengthscale,
hughes_water_prop.epsilonAB, hughes_water_prop.kappaAB,
hughes_water_prop.epsilon_dispersion,
hughes_water_prop.lambda_dispersion,
hughes_water_prop.length_scaling, mu_satp));
f = constrain(constraint, f);
// constraint.epsNativeSlice("papers/hughes-saft/figs/single-rod-in-water-constraint.eps",
// Cartesian(0,ymax,0), Cartesian(0,0,zmax),
// Cartesian(0,ymax/2,zmax/2));
//printf("Constraint has become a graph!\n");
potential = hughes_water_prop.liquid_density*constraint
+ 1000*hughes_water_prop.vapor_density*VectorXd::Ones(gd.NxNyNz);
//potential = hughes_water_prop.liquid_density*VectorXd::Ones(gd.NxNyNz);
potential = -hughes_water_prop.kT*potential.cwise().log();
Minimizer min = Precision(1e-11, PreconditionedConjugateGradient(f, gd, hughes_water_prop.kT,
&potential,
QuadraticLineMinimizer));
//printf("\nDiameter of rod = %g bohr (%g nm)\n", cavitysize, cavitysize/nm);
const int numiters = 50;
for (int i=0;i<numiters && min.improve_energy(false);i++) {
fflush(stdout);
//Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
//density.epsNativeSlice("papers/hughes-saft/figs/single-rod-in-water.eps",
// Cartesian(0,ymax,0), Cartesian(0,0,zmax),
// Cartesian(0,ymax/2,zmax/2));
// sleep(3);
}
const double EperCell = EperVolume*(zmax*ymax - 0.25*M_PI*cavitysize*cavitysize)*width;
//printf("The bulk energy per cell should be %g\n", EperCell);
double energy = (min.energy() - EperCell)/width;
//printf("Energy is %.15g\n", energy);
fprintf(o, "%g\t%.15g\n", cavitysize/nm, energy);
char *plotname = (char *)malloc(1024);
sprintf(plotname, "papers/hughes-saft/figs/single-rod-res0.5-slice-%04.1f.dat", cavitysize/nm);
Grid density(gd, EffectivePotentialToDensity()(hughes_water_prop.kT, gd, potential));
plot_grids_y_direction(plotname, density);
free(plotname);
}
fclose(o);
}
